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Solving systems of equations over commutative rings
Seidl, Jan ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The object of this work is to offer algorithm how can be solved systems of linear equations Ax=b over principal ideal rings. We prove that for every nonzero matrix over principal ideal rings there exists its Smith form. Using Smith form we transform the system of equations to simple diagonal form and we show how we can obtain the solution of the original system from its diagonal form. Whole procedure we demonstrate by the examples over Z, Zm and Q[x]. Thereafter we show how is possible to implement the algorithm for these rings by using software Mathematica. The work should provide procedure according to which shold not be difficult to modify algorithm to gain solution over another rings. 1
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Polynomial equations over finite fields and algebraic cryptanalysis
Seidl, Jan ; Stanovský, David (advisor) ; Drápal, Aleš (referee)
Title: Polynomial equations over finite fields and algebraic cryptanalysis Author: Jan Seidl Department: Department of Algebra Supervisor: doc. RNDr. David Stanovský, Ph.D., Department of Algebra Abstract: The present work deals with the procedure of algebraic crypta- nalysis, in which the problem of breaking cipher is at first converted to the problem of finding solutions to polynomial systems of equations and then the problem of finding a solution to this equation is converted to the SAT problem. The work specifically describes the methods that allow you to con- vert the problem of breaking cipher RC4 to the SAT problem. The individual methods were programmed in Mathematica programming language and then applied to RC4 with a word length of 2, 3. For finding of satisfiable evaluation of the resulting logical formula was used SAT-solver CryptoMiniSAT. In case of RC4 with word length 2 the solution was reached in the range from 0.09 to 0.34 second. In case of RC4 with word length 3 the solution was reached in the range from 1.10 to 1.23 second. Keywords: RC4, SAT, CryptoMiniSAT 1
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Homosexuality in the Praxis and Discourse of Penal Law, Medicine and Civic Society from the Adoption of the 1852 Penal Code to the Adoption of the 1961 Penal Code
Seidl, Jan ; Putna, Martin (advisor) ; Sokolová, Věra (referee) ; Nečasová, Denisa (referee)
This thesis deals with changes in conceptions of homosexuality and homosexual subculture as of something basically different, as they developed from the second third of the 19th century to the second half of the 20th century among Czech lawyers and physicians, as well as with changes of self-conceptualization of the Czech homosexual subculture itself, having occurred in the same time interval. It focuses mainly on attitudes and efforts of those who aimed at contributing to social emancipation of this subculture or - in times of increased persecution of homosexuality during the Nazi occupation - on the impossibility to carry on such efforts. The thesis is divided in five parts - in the first one, the legal context which provoked the emancipation efforts in times of the 1852 Penal Code being in force (i.e. until 1950) is explained; the next four parts focus on these efforts separately in four distinct periods. Thus, the second part deals with the expansion of the modern concept of homosexual identity in the Czech lands before WWI, the third part deals with sexual reform efforts by liberal lawyers and physicians as well as on emancipatory and political efforts by the homosexual community itself in the democratic First Czechoslovak Republic (1918-1938), aiming at decriminalization of homosexual acts,...
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Polynomial equations over finite fields and algebraic cryptanalysis
Seidl, Jan ; Stanovský, David (advisor) ; Drápal, Aleš (referee)
Title: Polynomial equations over finite fields and algebraic cryptanalysis Author: Jan Seidl Department: Department of Algebra Supervisor: doc. RNDr. David Stanovský, Ph.D., Department of Algebra Abstract: The present work deals with the procedure of algebraic crypta- nalysis, in which the problem of breaking cipher is at first converted to the problem of finding solutions to polynomial systems of equations and then the problem of finding a solution to this equation is converted to the SAT problem. The work specifically describes the methods that allow you to con- vert the problem of breaking cipher RC4 to the SAT problem. The individual methods were programmed in Mathematica programming language and then applied to RC4 with a word length of 2, 3. For finding of satisfiable evaluation of the resulting logical formula was used SAT-solver CryptoMiniSAT. In case of RC4 with word length 2 the solution was reached in the range from 0.09 to 0.34 second. In case of RC4 with word length 3 the solution was reached in the range from 1.10 to 1.23 second. Keywords: RC4, SAT, CryptoMiniSAT 1
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Homosexuality in the Praxis and Discourse of Penal Law, Medicine and Civic Society from the Adoption of the 1852 Penal Code to the Adoption of the 1961 Penal Code
Seidl, Jan ; Putna, Martin (advisor) ; Sokolová, Věra (referee) ; Nečasová, Denisa (referee)
This thesis deals with changes in conceptions of homosexuality and homosexual subculture as of something basically different, as they developed from the second third of the 19th century to the second half of the 20th century among Czech lawyers and physicians, as well as with changes of self-conceptualization of the Czech homosexual subculture itself, having occurred in the same time interval. It focuses mainly on attitudes and efforts of those who aimed at contributing to social emancipation of this subculture or - in times of increased persecution of homosexuality during the Nazi occupation - on the impossibility to carry on such efforts. The thesis is divided in five parts - in the first one, the legal context which provoked the emancipation efforts in times of the 1852 Penal Code being in force (i.e. until 1950) is explained; the next four parts focus on these efforts separately in four distinct periods. Thus, the second part deals with the expansion of the modern concept of homosexual identity in the Czech lands before WWI, the third part deals with sexual reform efforts by liberal lawyers and physicians as well as on emancipatory and political efforts by the homosexual community itself in the democratic First Czechoslovak Republic (1918-1938), aiming at decriminalization of homosexual acts,...
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Solving systems of equations over commutative rings
Seidl, Jan ; Šťovíček, Jan (advisor) ; Žemlička, Jan (referee)
The object of this work is to offer algorithm how can be solved systems of linear equations Ax=b over principal ideal rings. We prove that for every nonzero matrix over principal ideal rings there exists its Smith form. Using Smith form we transform the system of equations to simple diagonal form and we show how we can obtain the solution of the original system from its diagonal form. Whole procedure we demonstrate by the examples over Z, Zm and Q[x]. Thereafter we show how is possible to implement the algorithm for these rings by using software Mathematica. The work should provide procedure according to which shold not be difficult to modify algorithm to gain solution over another rings. 1
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